1. Field of the Invention
This invention relates to the field of nuclear magnetic resonance (NMR) spectroscopy and, more particularly, to a method for analyzing the composition of a solution using an inversion recovery Fourier transform (FT) technique.
2. Prior Art
Pulse-actuated FT NMR spectrometers are well known in the prior art. Such instruments conventionally include a holder for positioning a sample to be analyzed in a strong homogenous unidirectional magnetic field. An intense pulse of radio frequency (RF) energy is applied to the sample for a short period of time, the pulse being a mixture of different frequencies operative to excite different resonant groups with the sample and produce a free induction decay (FID) signal. Several FID signal measurements are commonly made to time average data points and improve the signal-to-noise (S/N) ratio. The FID signal is an analog one and it is commonly digitized so that a conventional digital computer can be used to perform a fast FT to produce a frequency domain spectrum of the FID signals. The spectrum can be used for both a quantitative and qualitative analysis of the sample.
One of the difficulties in the use of NMR spectrometers arises when attempting to analyze a sample consisting of a solution containing organic compounds dissolved in a solvent containing nuclei of the type excited by the RF pulse. This commonly occurs in the proton analysis of compound mixture dissolved in water where the hydrogen nuclei or protons of the water are more abundant and produce a much stronger spectral line than that produced by the compounds of interest. In other words, in the spectrum, the peak due to the solvent is much higher, often by a factor of from ten-to-one to one-hundred-to-one or more, than the peak or peaks of the solute. The smaller solute peaks are then more difficult to analyze. Additionally the solvent peak may overlap or hide a solute peak of interest.
To avoid the above difficulty, an inversion recovery technique may be used. This technique is known and is described in the article "Measurement of Spin Relaxation in Complex Systems," by R. L. Vold et al, J. Chem Phys. Vol. 48 (1968), pages 3831-3832. In accordance with this technique, a series of pulse sequences of 180.degree. and 90.degree. pulses are applied with variable times between the pulses, to obtain a spectra of the magnetization vector Mz along the Z-axis for each component of the spectrum. One of the spectra thus produced includes the condition that the magnetization of the solvent peak is substantially zero and therefore the solvent peak is eliminated from the spectrum. Thus, the remaining peaks are those of only the compounds undergoing analysis. To our knowledge, the use of such technique in the prior art has been limited to providing a qualitative analysis of the compounds and the technique has not been used in connection with a quantitative analysis particularly in the manner of our invention, as discussed in detail below.
Various quantitative analytical NMR techniques are known in the prior art including one in which a spectrum is analyzed by dividing the spectrum into regions containing the various peaks, the number of regions being equal to or greater than the number of compounds in the mixture under analysis. The areas under the peaks in such regions are determined and then the concentrations of the compounds are calculated in accordance with a set of linear equations defined by: ##EQU1## where A.sub.i = area of spectral region i
a.sub.ij = area of spectral region produced by a concentration of 1 gram per ml. of compound j PA1 f.sub.j = concentration of compound j (g/ml), i.e., the fraction of 1 g/ml which the concentration of compound j represents in the mixture. PA1 N = number of compounds
Equation (1) may be written in matrix form as: EQU A = a F (2) EQU f = a.sup.-1 A (3)
equation (3) represents the matrix solution. For an example, where there are two compounds in the mixture, the explicit solutions are: ##EQU2##
This general technique is described in "High Resolution NMR," by E. Becker, Chapter 12, 1969, Academic Press, New York, and in references cited therein. To our knowledge, such quantitative analysis has not been used in conjunction with the inversion recovery technique probably because quantitative analytical capabilities have not been introduced on commercial systems.